Automatic binary calculating machine for matricial calculation



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Patented June 1, 1954 AUTOMATIC BINARY CALCULATING MA- CHINE FORMATRICIAL CALCULATION Jean Grosvalet, Anbony, and Jean Simon-Suisse,Douala, France, assignors to Ofiice National dEtudes et de RecherchesAeronautiques, Paris, France, a corporate body of France Application May7, 1948, Serial No. 25,696

Claims priority, application France May 14, 1947 3 Claims. 1

Our invention relates to a calculating machine for matricial calculationand particularly to a machine adapted to multiply automatically a matrixby a column matrix.

An object of our invention is to provide a calculating machine adaptedto sum up two or several algebraic numbers.

Another object of our invention is to provide a calculating machineadapted to translate decimal data into binary data.

Another object of our invention is to provide a calculating machineadapted to multiply two or several algebraic numbers.

Another object of our invention is to provide a calculating machineadapted to multiply a matrix by a column matrix.

Another object of our invention is to provide a calculating machineadapted to translate binary results into decimal results.

Before disclosing the calculating machine and the structure of theunits, which when suitably associated, may perform such operations, itis desirable to recall to mind the rules of multiplication of a matrixby a column matrix.

A square matrix of order n is an array of n values arranged in columnsand in rows and termed the elements. For instance is a square matrix ofthird order.

We will designate a square matrix by the symbol [M], the general elementof this matrix being (11k (7 being the number of the row, and 7c thenumber of the column) A column matrix is constituted by a single column;for instance is a column matrix which we will call hereinafter moresimply a column. We will designate a column by the symbol [Y], thegeneral element of this column being 1 (9 being the number of the row).

lhe product of a matrix [M] by a column [Y] is a column [C] the elementsof which are formed by the rule 2 Example:

The foregoing and other objects of our invention Will clearly appear inthe following detailed description when studied in connection with theaccompanying drawings, wherein:

Figs. 1 and 2 represent a number indicator for the storage of binarydata and results;

Fig. 3 represents an idealized number indicator;

Fig. 4 represents an idealized revolution counter used in the machine;

Figs. 5 and 6 represent the totalizer of the machine;

Fig. 7 represents the rotative commutator associated with the totalizer;

Figs. 8 and 9 represent the positioning keyboard for data location;

Figs. 10, 11, 12, 13, 14:, 15a, 15b and represent. the posting key-boardand decimal-binary data transformer for data storage;

Fig. 16 represents partially the decimal binary transformer;

Figs. 17, 18 and 19 represent the binary decimal results transformer;

Fig. 20 represents the decimal results registering means;

Fig. 21 represents the matrix-matrix-column multipler circuit;

Figs. 22 and 23 represent symbolised relays;

Fig. 24 represents the machine control means;

Fig. 25 represents the block-diagram of the machine.

Number indicator of a binary number (Figs. 1, 2, 3)

A number indicator comprises a plurality of open or closed contacts,each of said contacts symbolizing a digit of a binary order of thenumber stored in said number indicator. In order to utilize said numberin the machine, current is sent unto the common input of said contacts;said number is then symbolized by the presence or absence of current inconductors connected to the outputs of these contacts.

In Figs. 1 and 2, shaft 5 is continuously driven by a motor group notshown. On said shaft are mounted flanges 2 and 3 forming the bearing ofthe shaft. Shaft l is composed of jointed sections allowing easydismantling. Flang 2 bears, by means of a circular crown 4, 41 pairs ofblades signed to cause the bending of blade 5. Armai ture 6 beingattracted, catch Hi, forced back by spring if, holds armature ii in thisposition. Catch in is provided with a projection portion 38 whichprevents armature from making contact with the core of electro-magnet l.

Electra-magnet 'e', rigidly fixed on arm i4 mounted free on shaft i isnormally stationary. Bar I5 which is U shaped, is pinned at 26 on arm Il and carries an armature and a double projection finger Ii. Said doubleprojection finger sinks into a recess provided to this effect in flange3 when the number indicator is at rest. Said recess is lined with arubber ring is. Projection finger I? is maintained in aforementionedrecess by pressure of spring 59 centered and supported by screw 2!securing guide 22 of bar 15.

Plate 23, comprising circular recesses on the same radius as projectionfinger ii, is continuously driven by shaft I by means of a pin. Theelectro-magnet terminals are connected to brushes 24 and rigidly fixedup on arm i l. Brush 2Q wipes circular conductive crown 28.

rigidly fixed on insulating crown 2i secured to flange 2 by threestandards 28.

Crown 2? comprises 24 pins 2% having between them the same angulardistance as the blades 5, 5 and 8, the position of a pin 29 being suchthat, in relation to the geometric dimensions of the number indicator,when brush 25 is in front of a given pin 29, the core of electro-magneti is in front of armature E of the corresponding blade 8.

Among the aforementioned 24 pins, 22 serve for registering binarydigits, one for registering the algebraic sign of the binary numberformed by It is evident that if the registering of binary numberscomposed of n binary digits is concerned, crown 2? will have n+2 pins 29and flange 2 n+1 groups of blades 5, 5' and ii.

In the inoperative position, projection finger l'l sinks into the rubberlined recess 83 and brush 25 is in front of starting pin 29. Th sendingof an electric current impulse on starting pin 29 causes armature I 6 tobe attracted by the electromagnet core. It will be noted that in theinoperative position there is no armature 6 at the other side ofelectro-magnet 1. Projection finger 'I'E sinks into one of the recessesof plate 23 and consequently drives arm is in rotation with itself.Brush 25 wipes successively all pins 29 and, depending on whether saidpins are provided with current or not, e1ectro-magnet 7 attracts or notcorresponding armatures 5 which close or not the contacts of blades 5and 5. Projection 33 raises each of catches i6 before electro-magnet iis in front of the corresponding blades which has for effect the openingof the contact that mai have been closed during the preceding rotation.When the driven mechanism has made a revolution, projection finger H isagain in front of recess i8 and, since no impulse is applied to thestarting pin, the mechanism becomes stationary as armature i6 is nolonger attracted. It will be noted that flange 3 performs the functionof flange 2 for the preceding number indicator, and flange 2 that offlange 3 for the following number indicator.

The number indicators are mounted by group on the same axis, and theflanges are rigidly fixed by a system of three threaded rods 34,provided with nuts 35 securing said flanges and allowing, in conjunctionwith joints 36 of shaft l, the removal of a number indicator from agroup without dismantling the others.

Symbolization of number ind cators For the following part of the presentdescription it is essential to be able to symbolize a number indicator.This symbolization is represented on Fig, 3. A number indicator for thestorage of the element as: of the matrix is designated by the notationCjk. All blades 5, 5 of number indicator C11; are connected in parallelto binding post LCjk.

The outgoing lead of a registering blade 5 terminates on binding post ZCjk, the index n denoting the binary order of the digit in the binarynumber registered. The binding post for the sign is designated by Z Cjk.

The input binding post of crown 26 is binding post 0 and is assumed inthe following description as permanently connected to the negative poleof the battery. Starting pin 29 is connected to binding post dCjk- Theinput binding post of a pin 29 is e cjk for the recording of a binarydigit and e Cjk for the recording of the sign.

In short a number indicator has 24 input binding posts, 8 051; to 6 051;for recording of 22 binary digits, e Cjk. for recording of the sign,dCjl: for starting the recording operation and 24 output binding posts Z0 1; to 1 011: for transmitting of 22 binary digits, Z Cjl: fortransmitting of the sign, L0 1; for starting the transmitting operation.0 is a permanent feeding binding post. It should be noticed that therecording operation is of the series type and the transmitting operationof the parallel type.

The recording of a number on a number indicator is effected in thefollowing manner:

Currents symbolizing binary digits (presence of current for the digit 1,absence of current for digit 0) arrive or not on pins c ear to 6 03};and the current symbolizing the sign (presence of current for signabsence of current for sign arrives or not on pin e cjk reserved for thesign. By sending a starting impulse to the pin connected to binding post(lop; there is thereby caused the rotation of electro-magnet l and thiselectro-magnet is energized or not according to whether brush 25 wipes apin 29 fed with current or not, and consequently closes or not thecorresponding contact 5-5.

The transmitting of the number recorded on the number indicator will beperformed by feeding with current binding post Lo r. A current appearson terminal Z Cjk if the digit of binary order n of the number stored isl and no current will appear if the digit of binary order n of thenumber stored is 0.

Block diagram of the machine (Fig. 25)

In the example chosen for the description of its general functioning,the machine comprises: Nine number indicators termed C11, C12, C12, C21,C22, C23, C31, C32, C33 for the storage of elements (in, (Z12,(Zia-(Z21, 1122, (I23, G31, 1232, ass of a matrix of the third order.

Three number indicators termed m1, m2, ms for the storage of elements.111, 112i 213 of a three elements-column-matrix. Theinput terminals ofsaid number indicators are designated by e m; to e mj, e mj and dmj andthe output terminals by l m to 1 m, l mj and Lmj wherein i=1, 2, 3.

Three number indicators termed pl, 102, pa for the storage of theelements of the product [C] =[Ml [Y]. The input terminals of said numberindicators are designated by e m to 9 13;], e pj and dpj and the outputterminals by l to 1 Z pj andL wherein i=1, 2, 3.

Fig. 25 relates to number indicators C 1; and m of a capacity of tenbinary orders plus a signand number indicators p of a capacity of 22binary orders plus a sign;

Referring again to Fig. 25, I (see Figs. to 16) designates a postingkeyboard on which are posted, in the decimal base, the matrix andcolumn-matrix data. The ten outputs of the posting keyboard areconnected, through leads 210i, to the input terminals biz to 1122 oftotalizer II (see Figs. 5 or 6). Posting keyboard I, associated withtotalizer II, transformsthe decimal data into binary data which becomeavailable upon terminals em to an of totalizer II. These terminals areconnected in parallel to input terminals of number indicators Cu to C33and m1, m2, me, through leads 2702, 2703, 2704.

A positioning keyboard III (see Fig. 8) directs the binary dataavailable at the output of totalizer II towards one of the numberindicators It comprises twelve Cu to C13 and m1, 1112, ms. keys,corresponding to the twelve number indicators and is connected throughleads 2195 and 2196 to the starting terminals of said number indicators.It sends an impulse to the chosen number indicator upon which the binarydata is stored.

A multiplier circuit IV (see Fig. 21) has two inputs, the firstconnected to the outputs of the matrix data number indicators 011 to C33through leads 2161, the second connected to the outputs of thecolumn-matrix data number indicators m1, m2, m3 through leads 22198.Circuit IV has two outputs, the first comprising 19 terminals which areconnected, through leads 2169, respectively to input terminals In to bigof totalizer II, the second comprising three terminals which areconnected, through leads 27m, to the starting terminals d 11, the, al sof number indicators 10;, 102, ps. The product elements appearsuccessively on output terminals e1 to 622 and es of totalizer II whichare'connected in parallel, through leads 2162 and 27! l, to the input ofnumber indicators 221, 102, pa. Circuit IV sends successive impulses todpl, d z, (1123 and 121, 132, pa successively store the elements of theproduct-column.

A binary-decimal transformer V (see Figs. 17, 18 and 19) transforms inthe decimal base, the product elements stored upon number indicators 21, 112, 103. It is connected to the output of said binary numberindicators through leads 2112.

It should be noticed that the number indicators are connected inparallel to the output terminals of totalizer II. This arrangement hasno inconvenience since the result is only stored upon the numberindicator (8) which makes a revolution after the result has becomeavailable and before it is erased.

Algebraic sum of two or several binary numbers Following is adescription of the algebraic adding operation of several binary numbers,which is one of the basic operations in the machine, and which-will beexplained by reference to the summing of any quantity of positive ornegative binary numbers, the sum of which does not exceed 22 binarydigits maximum.

Fig. 5 is the wiring diagram of a plurality of relays forming threeregisters 500, 540 and 583.

Ineach register, the place of a relay corresponds to the order of abinary digit; for example, relays 502, 54-2 and 582 correspond to binaryorder 1 (second digit from right). The position of the blades correspondto the value of the digit, 0 when the relay is off, 1 when the relay ison. Figs. 22 and 23 are the symbols of such relays.

Fig. 22 shows a single winding relay. Fig. 23

represents a memory relay with two windings, the lowest one being theholding winding. The terminal of a relay shown free on a diagram issupposed to be connected to the negative terminal of the battery.

Commutatorlill of Fig. 7 controls the operations in said registers 500,540 and 580. The first action of this commutator is to allow one binarynumber to be recorded on register 5%. The plurality of currentsrepresenting this number (one current for digit 1, no current for digit0) is sent to terminals 131 to 1219 or big to Z722 as shown in Figs. 5and 25, and energizes or not corresponding relays 5i?! to 522.

On register 5 3i) is recorded another binary number which is 0 at thebeginning of the adding operation.

The next action of commutator it! is to send a current in terminal E ofFig. 5, which current will trigger the adding operation, the sum beingrecorded on register 581].

Then, the further action of commutator it! is to transfer the sum fromupper register 535 to medium register 540 and to rub out the numberrecorded on register 506 which is now ready for receiving the nextnumber to be added. The cycle, so terminated, begins again.

Finally, the last result is recorded on terminals e1 to cm of upperregister 580.

The adding operation itself will now be explained in details. Topositive numbers to be added are supposed to be recorded on registers528 and 540 respectively. On Fig. 5, each column of relays correspondsto a definite order of the digits of the numbers recorded.

Now, let us see what happens when the adding operation is triggered by acurrent applied on terminal E. This current runs from right to left andreaches column-of relays 5E2, 542 and 582, chosen for detailedexplanations, by lead 5M or 532 according to the absence or the presenceof carry over from the preceding column.

Istcasa-The digits recorded on 582 and 542 are 0 and 0 and there is nocarry over coming from the preceding column.

Relays 562 and 542 are de-energised; according to the absence of carryover, current applied on terminal E comes by 53! from the precedingcolumn, goes through relay 5tl2 by blade 562i oiT, through relay 552 byblade 542-3 off and leaves the column by lead 533. Rectifier 5H preventssaid current from energising medium winding of upper relay 582 throughlead 513. The result recorded on this column of register 523i! istherefore 0 and the following column is subjected to the same conditionas the column heretofore mentioned, arrival of current by lead 533characterising absence of carry over.

2nd case-The digits recorded on 502 and 542

